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论文类型：期刊论文

发表时间：2013-01-01

发表刊物：SIAM JOURNAL ON NUMERICAL ANALYSIS

收录刊物：SCIE、Scopus

卷号：51

期号：5

页面范围：2680-2699

ISSN号：0036-1429

关键字：semilinear elliptic equation; eigenfunction expansion discretization; error analysis; polynomial system; homotopy continuation; spurious solution

摘要：Eigenfunction expansion discretization is considered for finding multiple solutions of semilinear elliptic equations with polynomial nonlinearity. Error estimates of the discretization are derived. An efficient polynomial homotopy is constructed for computing all solutions of the resulting polynomial system on coarse level. A filter strategy on successively finer levels is designed to remove spurious solutions and to refine nonspurious solutions, simultaneously. The filtered solutions are further refined by a finite element Newton method. Numerical results are included to verify the error estimates derived, the efficiency of the homotopy, and the effectiveness of the filter strategy. A specific case of the Lazer-McKenna conjecture is numerically verified.